The labial class is the last of the five, and reaching it completes the movement the consonant order is built on: a run from the back of the mouth to the front, class by class, from the soft palate to the lips. That single organising idea is what makes the Indian consonant order different in kind from the alphabets of western Asia, whose sequences preserve an inherited order with no phonetic logic behind it at all.
The grammarians name this class from the word for lip, and they place the two u vowels in the same family, since those too are made with the lips rounded. That cross-reference between the vowel table and the consonant table is deliberate. The four semivowels are likewise paired with four of the vowels, so the two halves of the order are tied together by the analysis rather than merely placed one after the other.
After the labials the order turns to the semivowels, the sibilants and the aspirate, and the arrangement changes principle: those groups are ordered by manner rather than by place. The join is visible in the table and it is one of the few places where the Indian scheme has to compromise, because a sound like the aspirate has no point of articulation in the mouth to be filed under. The tradition put it last, on the reasoning that there is nowhere further back to go.